ASTRONOMICAL FORMULAE
APERTURE where d is the aperture of the objective where M is the magnification Apparent Field: the closest
separation eye can see is 4', more True Field (in °) = 0.25
* time * cos of the declination
At prime focus (ground glass), magnification is 1x for MAGNIFICATION: BY DIAMETER AND EXIT
PUPIL where M is the magnification The scotopic (dark-adapted) aperture of the human pupil
is
(by substituting F/f for M) By substituting d=7 (the scotopic aperture of the human
pupil) LOW-POWER LAW FOR LIMITING MAGNIFICATION (by substituting 6 mm for d and taking the reciprocal)
(by substituting 0.63 mm, the minimum diameter to which
the where M is the maximum theoretical magnification (158x
per mm LIMITING VISUAL MAGNITUDE (LIGHT-GATHERING
POWER) where m is the approximate limiting visual magnitude RELATIVE LIGHT EFFICIENCY (TWILIGHT
FACTOR) where the larger the relative brightness value, the better
(the second formula is based on Lambda = 0.00055 for yellow) LINEAR RADIUS OF AIRY (DIFFRACTION)
DISC where r is the linear radius (one-half the linear diameter)
where Theta is the smallest resolvable angle in " Atmospheric conditions seldom permit Theta < 0.5".
The Dawes
where M is the magnification required About the closest star separation that the eye can distinguish
where Resolution is the smallest resolvable lunar feature
in km
where Light Grasp is times that received by the retina To compare the relative light grasp of two main lenses used
at the F-NUMBER: PRIME FOCUS (ERECT IMAGE) where f/ is the f-number of the system (objective)
where f/ is the f-number of the system The diameter of the first image equals the film diagonal
where f/ is the f-number of the system
where f/ is the f-number of the system
(the ratio of intensities of illumination is squared where Exposure Compensation is the exposure compensation
where Exposure Compensation is the exposure compensation
(the light-recording power is directly proportional to the where Power is the light-recording power of the system Example: a 200-mm f/8 system compared with a 100-mm f/5
system
where Efficiency is the efficiency of the lens for
where Print EFL is the print's effective focal length
where Guidescope M is the magnification needed Experience indicates that the minimum guiding magnification
needed Guidescope M = Guidescope EFL / Print EFL where Guidescope M is the guidescope's magnification (should
be >=
where Guiding Tolerance is in mm
where S is the error ("slop") in " The slop is derived from the formula Theta = k*(h/F),
where EFL is the effective focal length in mm
where Resolving Power is the resolving power of a photographic
where Maximum Resolution is the resolution for a perfect
lens Most films, even fast ones, resolve only 60 lines/mm; the
human
where Minimum Resolution is the min resolution necessary
SIZE OF IMAGE (ANGULAR) where h is the linear height in mm of the image at prime
focus The first formula yields image size of the sun and moon
as The second formula can be used to find the angle of view
(Theta) The third formula can be used to find the effective focal
length LENGTH OF A STAR TRAIL ON FILM where Length is the length in mm of the star trail on film EXPOSURE TIME FOR STAR TRAIL ON 35-MM
FILM where T is the exposure time in minutes for a length of
24 mm
where T is the maximum exposure time in seconds without
a star F is the focal length of the lens in mm The earth rotates 5' in 20 s, which yields a barely detectable N.B. The above formulae assume a declination of 0o. For
other
where i is the linear image size in mm of the image at prime
focus h is the linear height of the object in units corresponding to D D is the distance of the object in units corresponding to h F is the effective focal length (focal length times Barlow The last formula gives the focal length necessary to photograph
a
where e is the exposure duration in seconds for an image
size of f is the f-number (f/) of the lens S is the film's ISO speed B is the brightness factor of the object (Venus 1000, Moon
125, Thus, a 2-minute exposure at f/1.4 is equivalent to a 32-minute SURFACE BRIGHTNESS OF AN EXTENDED
OBJECT ("B" VALUE) where B is the surface brightness of the (round) extended object M is the magnitude of the object (total brightness of the
object), D is the angular diameter of the object in seconds of arc
(D^2 is
where e is the exposure duration in seconds HOUR ANGLE where H is the hour angle The Hour Angle is negative east of and positive west of
the
where n is the serial order of the planets from the sun
(Mercury's
where Theta is the object's apparent angular size in units h is the linear height of the object in units corresponding to D D is the distance of the object in units corresponding to h Theta is the object's angular height (angle of view) in
units k is a constant with a value of 57.3 for Theta in degrees,
3438 in A degree is the apparent size of an object whose distance
is 57.3 Under ideal conditions, the human eye can resolve anything LENGTH OF A METEOR TRAIL where h is the linear height of the meteor in km GEOGRAPHIC DISTANCE where cos(Latitude)=1 on lines of constant longitude ESTIMATING ANGULAR DISTANCE Penny, 4 km distant .......................................
1"
Big Dipper, from cup to handle Little Dipper, from cup to handle RANGE OF USEFUL MAGNIFICATION OF A TELESCOPE D = diameter of aperture in mm Minimum useful magnification ....................
0.13*D 0.2*D for better contrast |